The need for efficient TFE arises especially in generating efficient math libraries for RISC (Reduced Instruction Set Computers) chips, CISC (Complex Instruction Set Computers) chips, digital signal processors (DSPs), and compilers. Present TFE systems typically utilize CORDIC (COordinate Rotation Digital Computer) computing techniques substantially as set forth by Jack E. Volder in The CORDIC Trigonometric Computing Technique, IRE Transactions on Electronic Computers, September, 1959, in A Unified Algorithm For Elementary Functions, by J. C. Walther, Spring Joint Computer Conference, 1971, or in Tien Chi Chen's techniques of U.S. Pat. No. 3,631,230 (1971).
Volder's utilization of the CORDIC technique sets forth two computing modes, rotation and vectoring, for trigonometric relationship determinations, depending on whether the coordinate components and angular argument of an original vector are given. Using a prescribed sequence of conditional additions or subtractions, Volder implements a CORDIC arithmetic unit to obtain a programmed solution of trigonometric relationships. Walther suggests that similar algorithms may be implemented for solution of exponentials by computing hyperbolic sine and hyperbolic cosine in the CORDIC rotation mode.
Walther utilizes a hardware fixed point processor to implement unifying algorithms containing CORDIC schemes. While the Walter unifying algorithms have been implemented since 1971, such algorithms are hampered by a low rate of convergence. Chen's method of computing exponentials essentially cuts the Taylor series to one term and utilizes that term for a series expansion. Chen's hardware implementation was formulated to remove multiplication operations and replace them with a single shift-add operation. Chen's algorithms require algorithmic iterations to provide an initial approximation to a function, requiring special purpose hardware for efficient implementation.
Further improvement in efficiently determining exponential values is needed.